Post-Fabrication Electrical Trimming of Silicon Bulk Acoustic Resonators using Joule Heating

This paper presents a new method to electrically trim the resonance frequency of a Silicon Bulk Acoustic Resonator (SiBAR) post fabrication. Width-extensional mode silicon resonators are heated by passing a current through their resonating elements. This causes a mass loading gold pattern to diffuse into the bulk of the resonator. Upon cooling, the gold diffusion increases the stiffness of the resonating structure slightly, which reflects as an upward shift in resonance frequency. Thus, silicon resonators can be permanently trimmed to a desired frequency value by an electrical calibration step. As a proof of concept, an upward frequency shift of 240 kHz is demonstrated for a 40% mass loaded 100 MHz SiBAR after one hour of Joule heating with 30 mA of DC current.